Mean-field model of the Verwey transition in magnetite

A mean-field model is applied to the Verwey transition in Fe_3(1-δ){O}₄$. Parametrization of the internal energy, in terms of the experimental dependence of transition temperature on metal-oxygen nonstoichiometry, yields results consistent with the existence of two regimes on either side of a critical composition δc=0.0039. For {δ}δc, first-order transitions occur, with singlet ground states and doublet excited states. For {δ}>δc, second-order transitions result, for ground and excited states of equal degeneracy. The density of states, determined by a single long-range-order parameter is used to calculate the Fermi potential of a free-electron gas and associated electrical transport properties, as a function of temperature and nonstoichiometry. The canonical cusp catastrophe describes critical behavior in the mean-field approximation.